Fidelity and entanglement close to quantum phase transition in a two-leg $XXZ$ spin ladder

TL;DR

This study investigates how fidelity susceptibility and entanglement entropy reveal quantum phase transitions in a two-leg XXZ spin ladder with rung coupling, highlighting the effectiveness of these measures in characterizing different phases.

Contribution

It provides a detailed analysis of the relationship between fidelity susceptibility, entanglement entropy, and quantum phase transitions in a two-leg XXZ spin ladder system.

Findings

Fidelity susceptibility effectively characterizes the transition between XY phases.

Entanglement entropy derivative predicts the transition from XY to rung singlet phase.

Quantum phase transitions are identified through these quantum information measures.

Abstract

The fidelity susceptibility and entanglement entropy in a system of two-leg $XXZ$ spin ladder with rung coupling is investigated by using exact diagonalization of the system. The effects of rung coupling on fidelity susceptibility, entanglement entropy and quantum phase transition are analyzed. It is found that the quantum phase transition between two different $XY$ phases can be well characterized by the fidelity susceptibility. Though the quantum phase transition from $XY$ phase to rung singlet phase can be hardly detected by fidelity susceptibility, it can be predicted by the first derivative of the entanglement entropy of the system.